My cat peed on my mouse cable

I would probably try swirling the connector in a bath of 90% or higher concentration rubbing alcohol to attempt to get rid of the contaminants in the urine that could corrode the metal in the connector. That stuff dries very quickly, so you can test it out shortly after. Urine on the cable itself shouldn't be an issue since the insulation ought to protect the wires inside; just wiping it down with the baby wipes should be good enough.

I'd suggest plugging it into a charging port first before plugging it into a computer. That way you'll know if there's a dead short; it may kill the mouse and/or the charger, but better that than the computer. If the optical tracking LED comes on, then there's a very good chance it survived and can be used again. Plug it into the computer and see what happens.